The frequency dependent capacitance-voltage (C-V) and conductance-voltage (G/ω-V) characteristics of Schottky barrier diodes (SBDs) with Cu contacts on Si doped GaAsN epilayers with (100) and (311) A/B orientations have been investigated in the frequency range from 20 kHz to 1 MHz at room temperature. C, G/omega and the deduced series resistance (R_s) show strong dependences on the applied frequency in the forward bias region, which is closely correlated to the frequency-dependent response of interface states (N_ss). In GaAsN SBDs with all three growth orientations, the increasing N composition is found to increase the peak value of capacitance and enhance its dependence on frequency, which thus implies a general rule that increasing N incorporation causes an increase in N_ss. The increasing extent of N_ss due to N incorporation, however, differs a lot for different growth orientations as analyzed by using Hill-Coleman method. It is revealed that (311)B is the promising growth orientation to suppress the N_ss generation over a wider N composition range in GaAsN Schottky devices. The reduced formation probability of non-substitutional N due to the efficient N incorporation on the (311)B plane is considered to be responsible for the observations.